Problem: Simplify the following expression: $z = \dfrac{1}{4y} - \dfrac{1}{7y}$
Solution: In order to subtract expressions, they must have a common denominator. The smallest common denominator is the least common multiple of $4y$ and $7y$ $\lcm(4y, 7y) = 28y$ $ z = \dfrac{7}{7} \cdot \dfrac{1}{4y} - \dfrac{4}{4} \cdot \dfrac{1}{7y} $ $z = \dfrac{7}{28y} - \dfrac{4}{28y}$ $z = \dfrac{7 -4}{28y}$ $z = \dfrac{3}{28y}$